The neutrino sector of the present model is enlarged by adding three gauge-singlet RHNs \(N_{i=1,2,3}^{c}\)  charged under \(D_{4}\times U(1)\)  group. These RHNs are responsible for generating the small neutrino masses via the type I seesaw mechanism as well as the BAU through the leptogenesis mechanism. The charges under \(D_{4}\times U(1)\)  of matter, Higgs and RHNs are listed in table (REF ). In this letter, the focus is put on the neutrino sector and
especially the study of the BAU; however, we should mention that in Ref.
[1]} where the charged fermion sector is studied as well, the Higgs
multiplets \(H_{\overline{45}}\)  and \(H_{24}\)  were also used to produce the
following ratios of the Yukawa couplings of the first and second generations
\(y_{e}/y_{d}=4/9\)  and \(y_{\mu }/y_{s}=9/2\)  which are in perfect agreement
with experimental data [2]}.
<TABLE>